Theories and applications of the large deviation principles for the mean-field model and the conservation laws
- This thesis considers the theories and applications of the large deviation principles for two model problems: one is a mean-field model for systemic risk and the other one is a scalar conservation law. In the systemic risk problem, I prove that individual risk does not affect systemic risk in an obvious way; that is to say, low individual risk does not unconditionally lead to low systemic risk, and in fact, it is possible to construct a system with low individual risk and high systemic risk at the same time. The conservation law problem considers the anomalous shift of a traveling wave due to space-time random perturbations; it becomes a large deviation problem as the random perturbations are small. I prove that the rate function, the rate of the exponential decay of the probability, is quadratic in the amount of the shift of the wave when the amount of the shift is small, and is linear in the amount of the shift if the amount is large. A large-deviation-based importance sampling Monte Carlo method is also implemented to compute the probability of the anomalous shift, and the numerical experiments show that it outperforms the basic Monte Carlo method.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Institute for Computational and Mathematical Engineering.
|Glynn, Peter W
|Glynn, Peter W
|Statement of responsibility
|Submitted to the Program in Institute for Computational and Mathematical Engineering.
|Thesis (Ph.D.)--Stanford University, 2012.
- © 2012 by Tzu-wei Yang
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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